Problem: Complete the square to solve for $x$. $x^{2}+14x+45 = 0$
Explanation: Begin by moving the constant term to the right side of the equation. $x^2 + 14x = -45$ We complete the square by taking half of the coefficient of our $x$ term, squaring it, and adding it to both sides of the equation. Since the coefficient of our $x$ term is $14$ , half of it would be $7$ , and squaring it gives us ${49}$ $x^2 + 14x { + 49} = -45 { + 49}$ We can now rewrite the left side of the equation as a squared term. $( x + 7 )^2 = 4$ Take the square root of both sides. $x + 7 = \pm2$ Isolate $x$ to find the solution(s). $x = -7\pm2$ So the solutions are: $x = -5 \text{ or } x = -9$ We already found the completed square: $( x + 7 )^2 = 4$